If $\frac{d y}{d x}=y+30$ and $y(0)=2$, then $y(\ln 2)$ is equal to

Question

If $\frac{d y}{d x}=y+3>0$ and $y(0)=2$, then $y(\ln 2)$ is equal to

Aicharya · Accepted Answer

$\frac{d y}{d x}=y+3 \Rightarrow \frac{d y}{y+3}=d x$ $\ln (y+3)=x+c$ $x=0 \Rightarrow y=2$ $\Rightarrow \ln 5=0+c$ $c=\ln 5$ $\ln (y+3)=x+\ln 5$ $y+3=e^{x+\ln 5} \Rightarrow y+3=e^{\ln 2+\ln 5}$ $y+3=10 \Rightarrow y=7$

If $\frac{d y}{d x}=y+3>0$ and $y(0)=2$, then $y(\ln 2)$ is equal to

Solution